A note on d-symmetric operators
1981 ◽
Vol 23
(3)
◽
pp. 471-475
Keyword(s):
An operator T on a complex Hilbert space is d-symmetric if , where is the uniform closure of the range of the derivation operator δT(X)=TX−XT. It is shown that if the commutator ideal of the inclusion algebra for a d-symmetric operator is the ideal of all compact operators then T has countable spectrum and T is a quasidiagonal operator. It is also shown that if for a d-symmetric operator I(T) is the double commutant of T then T is diagonal.
1974 ◽
Vol 26
(1)
◽
pp. 115-120
◽
1987 ◽
Vol 29
(1)
◽
pp. 99-104
◽
Keyword(s):
1985 ◽
Vol 26
(2)
◽
pp. 141-143
◽
Keyword(s):
Keyword(s):
1988 ◽
Vol 103
(3)
◽
pp. 473-480
Keyword(s):
2005 ◽
Vol 2005
(7)
◽
pp. 767-790
◽
1984 ◽
Vol 98
(3-4)
◽
pp. 291-303
◽
Keyword(s):